Mechanically programmable auxetic tubular metamaterials with enhanced energy absorption and negative Poisson's ratio for energy absorbing railway barrier foundations

Abstract

This study presents a novel tubular auxetic metamaterial with a curved C-shaped reentrant unit cell, designed to achieve tunable mechanical performance through controlled geometric variation. Five configurations, defined by the main arc diameter (1.5 to 10.5 mm), were analyzed using finite element simulations in Abaqus/Standard, and one representative sample (D3) fabricated by Digital Light Processing (DLP) 3D-printing using commercial K + photopolymer resin for experimental validation. The simulations revealed a nonlinear deformation trend: increasing the arc diameter enhanced both stiffness, from 80.13 to 429.90 N ${\mathrm{mm}}^{-1}$ , and specific energy absorption, from 40.30 to 220.30 J ${\mathrm{Kg}}^{-1}$ , up to an optimal curvature (D4), beyond which instability and local buckling emerged. The negative Poisson's ratio became more pronounced, decreasing from −1.14 to −2.33 with increasing curvature, driven by enhanced radial expansion and hinge-like rotation of the C-shaped arcs. Experimental results for D3 closely matched the simulation results, with a peak force of 432.6 N vs 427.3 N, confirming the predictive reliability of the model. The combination of high auxeticity, strong energy absorption, and controllable stiffness highlights the design's potential for impact-absorbing railway barrier systems, where directional stability and impact resistance are critical.